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If you sent out probes to calculate the travel time of beams of light between two points, but at Lagrange points from one another, and then had them simultaneously slow their orbits to fall into the sun, and considered the "edge" of the sun the point at which it destroyed the probes...

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How do you measure the diameter of the sun when your most advanced technology does not include a telescope. And even when it does, but just a telescope about 8x power (approx Gallileo’s first one)

That Copernicus got there at all is incredible

I feel like shadows are the "simple tech" path. It was known since ancient times you can get the circumference of the Earth (remarkably accurately) by doing some calculations based on the angles of shadows from the mid-day sun at two points sufficiently north/south from each other (a fantastic application of trig). Knowing the circumference of the Earth and these angles lets you know the diameter/radius as well which lets you create a "straight line" distance (i.e. not the over the surface distance) between those two points. Using those two points and known angles to construct a triangle with the Sun should let you see it is at least extraordinarily far away, even if your measurements are relatively innacurate.

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